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The steady-state approximation for the excited singlet givesand that for the triplet givesCombining these with the quantum yield definition gives the more general expressionUnder the supplied limit $k_{\mathrm{ISC}}\gg k_F$, this becomesThe approximation is the near-unit triplet formation yield, not an assumption that phosphorescence is the only triplet loss process.

Write $D=[\mathrm{C}{\mathrm{l}}_2{\mathrm{O}}_2]$ and $c=[\mathrm{ClO}]$. In the steady-state approximation for the dimer, chlorine peroxide chlorine peroxide formation is balanced by its two competing removal channels:The association event rate is $k_1[M]c^2$; the associated disappearance rate of chlorine monoxide is twice that value. Each successful photodissociation event produces two chlorine atoms after the subsequent fast fragmentation, and their return to chlorine monoxide consumes two ozone molecules. Thermal dissociation instead returns the dimer to two chlorine monoxide radicals without destroying ozone. Thus the chemical branching fraction for an ozone-destroying event is $f=J_2/(J_2+k_3[M])=0.7$, givingThis is the sunlit chlorine monoxide dimer cycle, with net conversion $2{\mathrm{O}}_3\to 3{\mathrm{O}}_2$. It assumes that the dimer relaxes rapidly, downstream fragmentation and chlorine–ozone reactions are sufficiently fast, and competing chlorine sinks can be neglected. Counting the formation event twice and then multiplying by two again would overestimate loss by a factor of two.

For the tropospheric OH budget, let $P$ be hydroxyl radical production per unit volume and $K$ its total first-order loss frequency. The present hydroxyl radical steady state hasHere one year is $365.25$ days; using it consistently makes the reported lifetimes in years independent of that conversion convention. Methane's chemical lifetime is ${\tau }_0=1/(k_2[\mathrm{OH}{]}_0)$, givingThe current combined loss frequency already includes existing hydrogen, so add only the incremental hydrogen sink:Holding production and the other losses fixed then gives $[\mathrm{OH}{]}_1=5.107\times 10^5\mathrm{molecules}\mathrm{c}{\mathrm{m}}^{-3}$ andThe rapid hydroxyl radical adjustment time, $1/K$ of order a second, supports its steady-state approximation in this box model. Subsequent methane growth would itself change hydroxyl radical consumption, so the computed increase is not a fully coupled long-term atmospheric prediction. Detailed molecular hydrogen modelling treats changes in methane, ozone and stratospheric water alongside reductions in other precursor emissions.^[ref]